"Let's try kimchi."
Can somebody explain the grammar point here please? I know 먹다 and -ㅂ시다 but 먹어보다..?
Basically adding 아/어/여보다 to a verb in the way it's done here gives it the meaning "to try to ____ (the original verb)" For example: 이것은 아직 안 먹어봤어요 - "I haven't tried to eat this" as in "I haven't tried this food".
A good way to remember this is that 보다 is "to see", so you can think of it as trying something "to see if you like it"! I don't think that has anything to do with the actual reason 보다 is used, but it might be helpful for remembering.
It is not.
세요 is polite form for imperative sentence, while ㅂ시다 is honorific form for propositive sentence.
Order =/= invitation
No, that's a command "try the kimchi (please)". Adding ㅂ시다/십시다 is the formal way of saying "let's"